Several years ago I waited until the first hot day of summer to turn on my AC. This is how I found out about one of the busiest times for repairmen and had to sweat for two weeks. Now I do a test run a couple of weeks before it heats up. Same goes for the furnace at the end of Autumn.
Relatedly: there are HUGE tax credits for heat pumps right now; I’m actually paying several thousand dollars less for a new heat pump than I would have for a new central AC. (Installed as a two stage system, so I can still use my regular boiler when it gets cold)
So if anybody else is up for a replacement you should definitely take a look at any federal + state + local credits you might get for going that route.
Having a boiler + heat pump would be a Hybrid system. A 2-stage heat pump typically refers to the capability for the heat pump to run at lower power (such as 70% max) or full power, to try and prevent thrashing on slightly warm days, while keeping capacity available for hot days.